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Subtraction without borrowing

Class 2 Class 3 CBSE UP Board

📘 What's inside:

Concept 1 — What is Subtraction Without Borrowing?

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When we subtract using the column method, sometimes the digit on top in a column is smaller than the digit below it. In that case we need to borrow from the next column — that is called subtraction with borrowing and is a separate topic.

In subtraction without borrowing, every digit of the minuend is greater than or equal to the digit of the subtrahend in the same column. This means we simply subtract each column directly — no borrowing, no extra steps.

The one rule to check: Before you start, scan each column. If every top digit ≥ bottom digit (O ≥ O, T ≥ T, H ≥ H), there is no borrowing needed and this method applies.
▶
Ones column: top digit ≥ bottom digit
e.g. 7 ≥ 3 ✓
▶
Tens column: top digit ≥ bottom digit
e.g. 5 ≥ 2 ✓
▶
Hundreds column: top digit ≥ bottom digit
e.g. 8 ≥ 4 ✓
⚠ How to Spot If Borrowing Is Needed

Scan each column before subtracting. If any column has the top digit smaller than the bottom digit (e.g. top = 3, bottom = 7), borrowing is required — that belongs to the next topic. All examples here are carefully chosen so every top digit is ≥ the bottom digit.

▶ Column Method — Steps (No Borrowing)
  • Write the minuend (larger number) on top.
  • Write the subtrahend (smaller number) directly below, aligning: Ones under Ones, Tens under Tens, Hundreds under Hundreds.
  • Write the − sign to the left of the subtrahend.
  • Draw a line under the subtrahend.
  • Subtract the Ones column first (right to left). Write the answer below the line.
  • Subtract the Tens column next. Write the answer.
  • Subtract the Hundreds column last. Write the answer.
  • Draw a double line under the answer. Read the difference.
```

Concept 2 — Subtracting 2-Digit Numbers (Without Borrowing)

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A 2-digit number has a Tens place and an Ones place. We subtract Ones first, then Tens.

▶ Solved Example 1
Find 57 − 23 using the column method.
TO
57
−23
34
O
Ones: 7 − 3 = 4. Write 4.
T
Tens: 5 − 2 = 3. Write 3.
  1. 1Write 57 on top, 23 below. T under T, O under O.
  2. 2Check: O → 7 ≥ 3 ✓   T → 5 ≥ 2 ✓. No borrowing needed.
  3. 3Ones: 7 − 3 = 4. Write 4.
  4. 4Tens: 5 − 2 = 3. Write 3.
57 − 23 = 34
▶ Solved Example 2
Find 89 − 46 using the column method.
TO
89
−46
43
O
Ones: 9 − 6 = 3. Write 3.
T
Tens: 8 − 4 = 4. Write 4.
89 − 46 = 43
▶ Solved Example 3 — Zero in Subtrahend
Find 75 − 30 using the column method.
TO
75
−30
45
O
Ones: 5 − 0 = 5. Subtracting 0 leaves the digit unchanged.
T
Tens: 7 − 3 = 4. Write 4.
75 − 30 = 45
▶ Solved Example 4 — Same Digit in a Column
Find 66 − 24 using the column method.
TO
66
−24
42
O
Ones: 6 − 4 = 2. Write 2.
T
Tens: 6 − 2 = 4. Write 4.
66 − 24 = 42

✍ Practice — Concept 2

Q1 Find using the column method: 78 − 35 ▼
Answer
TO
78
−35
43
O: 8−5=3   T: 7−3=4   Answer: 43
Q2 Find using the column method: 96 − 53 ▼
Answer
TO
96
−53
43
O: 6−3=3   T: 9−5=4   Answer: 43
Q3 Find using the column method: 87 − 50 ▼
Answer
TO
87
−50
37
O: 7−0=7   T: 8−5=3   Answer: 37
Q4 True or False: In 54 − 32, the Tens column is 5−3=2 and Ones column is 4−2=2. So the answer is 22. ▼
Answer True.
TO
54
−32
22
O: 4−2=2   T: 5−3=2   Answer: 22 ✓
Q5 Drill — solve all four: (a) 49−17   (b) 68−45   (c) 77−33   (d) 95−62 ▼
Answer
(a)
TO
49
−17
32
(b)
TO
68
−45
23
(c)
TO
77
−33
44
(d)
TO
95
−62
33
(a) 32   (b) 23   (c) 44   (d) 33
```

Concept 3 — Subtracting 3-Digit Numbers (Without Borrowing)

```

A 3-digit number has Hundreds, Tens and Ones. The method is exactly the same — subtract right to left: O → T → H.

▶ Solved Example 5
Find 587 − 243 using the column method.
HTO
587
−243
344
O
Ones: 7 − 3 = 4. Write 4.
T
Tens: 8 − 4 = 4. Write 4.
H
Hundreds: 5 − 2 = 3. Write 3.
  1. 1Align H, T, O. Check: 7≥3 ✓   8≥4 ✓   5≥2 ✓. No borrowing.
  2. 2Ones: 7 − 3 = 4.
  3. 3Tens: 8 − 4 = 4.
  4. 4Hundreds: 5 − 2 = 3.
587 − 243 = 344
▶ Solved Example 6 — Zero in Subtrahend
Find 796 − 304 using the column method.
HTO
796
−304
492
O
Ones: 6 − 4 = 2.
T
Tens: 9 − 0 = 9. Subtracting 0 leaves 9.
H
Hundreds: 7 − 3 = 4.
796 − 304 = 492
▶ Solved Example 7 — Larger Digits
Find 978 − 456 using the column method.
HTO
978
−456
522
O
Ones: 8 − 6 = 2. ✓
T
Tens: 7 − 5 = 2. ✓
H
Hundreds: 9 − 4 = 5. ✓
978 − 456 = 522
▶ Solved Example 8 — Zero in the Difference
Find 835 − 205 using the column method.
HTO
835
−205
630
O
Ones: 5 − 5 = 0. Write 0.
T
Tens: 3 − 0 = 3. Write 3.
H
Hundreds: 8 − 2 = 6. Write 6.

When the answer has a zero, always write the 0 — it is part of the difference. 630 ≠ 63.

835 − 205 = 630

✍ Practice — Concept 3

Q6 Find using the column method: 869 − 435 ▼
Answer
HTO
869
−435
434
O: 9−5=4   T: 6−3=3   H: 8−4=4   Answer: 434
Q7 Find using the column method: 748 − 506 ▼
Answer
HTO
748
−506
242
O: 8−6=2   T: 4−0=4   H: 7−5=2   Answer: 242
Q8 Riya says 654 − 321 = 333. Check her answer using the column method. ▼
Answer
HTO
654
−321
333
O: 4−1=3   T: 5−2=3   H: 6−3=3.   Yes, Riya is correct. 654 − 321 = 333.
Q9 Drill: (a) 567−234   (b) 899−465   (c) 777−444   (d) 690−350 ▼
Answer
(a)
HTO
567
−234
333
(b)
HTO
899
−465
434
(c)
HTO
777
−444
333
(d)
HTO
690
−350
340
(a) 333   (b) 434   (c) 333   (d) 340
```

Concept 4 — Word Problems

```

For word problems involving subtraction, look for words like left, remaining, less, difference, how many more, took away, spent, used. Write the subtraction sentence and solve using the column method.

▶ Steps to Solve a Subtraction Word Problem
  • Read the question fully.
  • Identify the minuend (larger amount) and subtrahend (amount taken away).
  • Check each column — is top digit ≥ bottom digit? (No borrowing needed.)
  • Solve using the column method.
  • Write the answer in a complete sentence.
▶ Solved Example 9 — 2-Digit
A shopkeeper had 86 pens. He sold 53. How many pens are left?
  1. 1Minuend: 86. Subtrahend: 53. Key word: left.
  2. 2Check: O → 6≥3 ✓   T → 8≥5 ✓. No borrowing.
TO
86
−53
33
O
6 − 3 = 3
T
8 − 5 = 3
The shopkeeper has 33 pens left.
▶ Solved Example 10 — 3-Digit
A library has 758 books. 325 are issued to students. How many books remain in the library?
  1. 1Minuend: 758. Subtrahend: 325. Key word: remain.
  2. 2Check: O→8≥5 ✓ T→5≥2 ✓ H→7≥3 ✓.
HTO
758
−325
433
O
8 − 5 = 3
T
5 − 2 = 3
H
7 − 3 = 4
433 books remain in the library.
▶ Solved Example 11 — How Many More
Class A has 689 students and Class B has 245 students. How many more students does Class A have?
  1. 1“How many more” = find the difference. Minuend: 689, Subtrahend: 245.
  2. 2Check: O→9≥5 ✓ T→8≥4 ✓ H→6≥2 ✓.
HTO
689
−245
444
O
9 − 5 = 4
T
8 − 4 = 4
H
6 − 2 = 4
Class A has 444 more students than Class B.

✍ Practice — Concept 4

Q10 Amit had ₹97. He spent ₹45. How much money does he have left? ▼
Answer
TO
97
−45
52
Amit has ₹52 left.
Q11 A factory made 875 toys. 342 were packed. How many toys are still unpacked? ▼
Answer
HTO
875
−342
533
533 toys are still unpacked.
Q12 A train has 968 seats. 745 are occupied. How many seats are empty? ▼
Answer
HTO
968
−745
223
223 seats are empty.
Q13 A bag had 599 marbles. 265 fell out. How many marbles are left? ▼
Answer
HTO
599
−265
334
334 marbles are left.
```
★ Key Points to Remember
  • In subtraction without borrowing, every top digit must be ≥ the bottom digit in its column.
  • Always write minuend on top, subtrahend below, aligned strictly: Ones under Ones, Tens under Tens, Hundreds under Hundreds.
  • Always subtract right to left: Ones first, then Tens, then Hundreds.
  • Subtracting 0 from any digit leaves that digit unchanged. (9 − 0 = 9)
  • When a column gives a difference of 0, write the 0 — never leave it blank. (805 − 205 = 600, not 6)
  • In word problems, key words like left, remaining, less, how many more, spent, used all indicate subtraction.

Exam Style — Class 2 & 3

5 Questions on Subtraction Without Borrowing

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Q1 Which of these can be solved without borrowing? Show working for the one(s) that can.
(a) 73 − 48    (b) 97 − 53    (c) 864 − 231 ▼
Answer (a) 73−48: O → 3 < 8 ✗ — borrowing needed. Cannot use this method.
(b) 97−53: O → 7≥3 ✓ T → 9≥5 ✓ — No borrowing.
(c) 864−231: O → 4≥1 ✓ T → 6≥3 ✓ H → 8≥2 ✓ — No borrowing.
(b)
TO
97
−53
44
(c)
HTO
864
−231
633
(b) = 44   (c) = 633
Q2 Solve showing full H, T, O working: 897 − 463 ▼
Answer
HTO
897
−463
434
O
7−3=4
T
9−6=3
H
8−4=4
897 − 463 = 434
Q3 A student solves 769 − 324 = 435. Check this answer. Is it correct? ▼
Answer
HTO
769
−324
445
O: 9−4=5   T: 6−2=4   H: 7−3=4. Correct answer = 445.
No, the student is wrong. The correct answer is 445, not 435. The student made an error in the Tens column (wrote 3 instead of 4).
Q4 A farmer had 876 kg of rice. He sold 345 kg at the market. How much rice does he have left? Write the subtraction sentence and solve. ▼
Answer Subtraction sentence: 876 − 345 = ?
Check: O→6≥5 ✓ T→7≥4 ✓ H→8≥3 ✓.
HTO
876
−345
531
The farmer has 531 kg of rice left.
Q5 Find the missing digit: 8_7 − 234 = 6_3. What are the two missing digits? ▼
Answer Let the missing Tens digit of minuend = a, missing Tens digit of difference = b.
O: 7 − 4 = 3 ✓ (matches answer Ones = 3).
H: 8 − 2 = 6 ✓ (matches answer Hundreds = 6).
T: a − 3 = b. We need a ≥ 3 (no borrowing). Try a = 7: 7 − 3 = 4. So b = 4.
HTO
877
−234
643
Missing digits: minuend Tens = 7, difference Tens = 4. Full problem: 877 − 234 = 643.
```
📄 Free Worksheet

Practise 2-digit and 3-digit subtraction without borrowing, including word problems and error-checking. No login required.

► Open Free Worksheet
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